Seismic Inversion Method Based on Logarithmic Three-dimensional Total Variation Sparse Constraint under Mixed-domain Constraints

The sparse impedance inversion method is widely used in oil and gas exploration. However, traditional sparse constraints capture limited three-dimensional spatial sparse information and often neglect the time-frequency characteristics of seismic data. As a result, the spatial resolution and accuracy of three-dimensional inversion results are often small. To address these limitations, this study proposes a seismic inversion method based on logarithmic three-dimensional total variation sparse constraints under mixed domain conditions. The method introduces a logarithmic penalty factor to extract sparse information. Compared with conventional sparse constraints, the logarithmic penalty allows for the extraction of more effective sparse structures. When combined with a 3D total variation constraint, this method fully exploits the spatial sparsity of wave impedance, thereby improving both spatial resolution and inversion accuracy. In addition, the proposed approach incorporates time-frequency domain information using a short-time Fourier transform (STFT) forward operator. This integration introduces essential time-frequency characteristics of seismic data into the inversion process, further enhancing its accuracy. To improve inversion stability, the method combines initial model constraints, time-frequency domain constraints, and logarithmic 3D total variation sparse constraints within a unified objective function. This objective function is solved using the alternating direction method of multipliers (ADMM). The proposed method was validated on both a three-dimensional thrust body model and real 3D seismic data. Results demonstrates that, compared to conventional methods, the proposed approach significantly improves the spatial resolution and accuracy of 3D inversion results.